In the American drill books "support arms" is just covered with the other positions with no real explanation.
In the Danish "tactics" a similar position is found in a chapter with "special positions"
"Gevær i arm" (support arms) is specifically used when a soldier is on guard duty.
This is a way of carrying the musket with the hammer resting on the left forarm with the right hand on the small of the stock.
The muskets sits well and both hands can be places close to the body next to or even covered by a lot of wool... rather important when on guard duty in cold weather...